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Applied Sciences

Pairing Hamiltonians of Nearest-Neighbor Interacting Superconducting Qubits on an IBM Quantum Computer

Shirshendu Chatterjee, Bikash K. Behera, Felix Jaetae Seo

Published Nov 6, 2023• 1 citation
Publisher

Abstract

A quantum simulation experiment pairing Hamiltonians of nearest-neighbor interacting superconducting qubits was performed with a complete set of algorithms on an IBM Quantum Computer-IBMq Lima. The experiment revealed that the fidelity is a function of iteration using Suzuki–Trotter decomposition for four different types of nearest-neighbor Heisenberg, XY, transverse, and longitudinal Ising superconducting qubit couplings of Hamiltonians. The experiment displayed the models of how the experimental density matrices shift from the theoretical density matrices and how their behavior changes with different numbers of iterations. It also demonstrated the reconstruction of quantum states and how the states change as a function of iteration with the IBM Quantum Computer-IBMq Lima. The time evolutions of the states for different models were also shown to predict the dominance of each state.

DOI
10.3390/app132112075

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A quantum simulation experiment pairing Hamiltonians of nearest-neighbor interacting superconducting qubits was performed with a complete set of algorithms on an IBM Quantum Computer-IBMq Lima. The experiment revealed that the fidelity is a function of iteration using Suzuki–Trotter decomposition for four different types of nearest-neighbor Heisenberg, XY, transverse, and longitudinal Ising superconducting qubit couplings of Hamiltonians. The experiment displayed the models of how the experimental density matrices shift from the theoretical density matrices and how their behavior changes with different numbers of iterations. It also demonstrated the reconstruction of quantum states and how the states change as a function of iteration with the IBM Quantum Computer-IBMq Lima. The time evolutions of the states for different models were also shown to predict the dominance of each state.
We present the quantum simulation of the frustrated quantum spin- 1 2 antiferromagnetic Heisenberg spin chain with competing nearest-neighbor ( J 1 ) and next-nearest-neighbor ( J 2 ) exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest-neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing the first-order Trotterization. Furthermore, our implementation of the second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era. Published by the American Physical Society 2024
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement ``quantum simulators.'' Quantum simulators are physical setups able to simulate other quantum systems efficiently that are intractable on classical computers. Based on solid-state qubit systems with various types of nearest-neighbor interactions, we propose a complete set of algorithms for simulating pairing Hamiltonians. The fidelity of the target states corresponding to each algorithm is numerically studied. We also compare algorithms designed for different types of experimentally available Hamiltonians and analyze their complexity. Furthermore, we design a measurement scheme to extract energy spectra from the simulators. Our simulation algorithms might be feasible with state-of-the-art technology in solid-state quantum devices.
Abstract We simulate the time-dependent dynamics of a three-site spin chain described by the Heisenberg XXX Hamiltonian. The quantum circuit representing the time-dependent wave function is constructed using the Suzuki-Trotter approximation, and is executed on the quantum computer ibm_kawasaki. At each time step, the density matrix of the three-qubit state is reconstructed by state tomography. By applying four different mitigation methods, Clifford data regression, Pauli twirling, density matrix purification, and density matrix orthogonalization, we demonstrate that accurate time-dependent populations and density matrices can be calculated on noisy superconducting-qubit type quantum computers.
The evolution of entanglement in a 3-spin chain with nearest-neighbor Heisenberg-XY interactions for different initial states is investigated here. In an NMR experimental implementation, we generate multipartite entangled states starting from initial separable pseudo-pure states by simulating nearest-neighbor XY interactions in a 3-spin linear chain of nuclear spin qubits. For simulating XY interactions, we follow algebraic method of Zhang et al. [Phys. Rev. A72 (2005) 012331]. Bell state between end qubits has been generated by using only the unitary evolution of the XY Hamiltonian. For generating W-state and GHZ-state a single qubit rotation is applied on second and all the three qubits, respectively after the unitary evolution of the XY Hamiltonian.
The simulation of complex quantum many-body systems is a promising short-term goal of noisy intermediate-scale quantum (NISQ) devices. However, the limited connectivity of native qubits hinders the implementation of quantum algorithms that require long-range interactions. We present the outcomes of a digital quantum simulation where we overcome the limitations of the qubit connectivity in NISQ devices. Utilizing the universality of quantum processor native gates, we demonstrate how to implement couplings among physically disconnected qubits at the cost of increasing the circuit depth. We apply this method to simulate a Floquet-driven quantum spin chain featuring interactions beyond nearest neighbors. Specifically, we benchmark the prethermal stabilization of the discrete Floquet time-crystalline response as the interaction range increases, a phenomenon never observed experimentally. Our quantum simulation addresses one of the significant limitations of superconducting quantum processors, namely, device connectivity. It reveals that nontrivial physics involving couplings beyond nearest neighbors can be extracted after the impact of noise is properly taken into account in the theoretical model and consequently mitigated from the experimental data. Published by the American Physical Society 2024
Among all the quantum computer candidates, the superconducting system is one of the most convincing platforms due to its strong couplings and scalability. To be more specific, this thesis focuses on the superconducting system, in which the artificial atoms are controlled longitudinally and coupled without any intermediate devices. We propose a superconducting decoupling method in this thesis. Firstly, we state that our algorithm can effectively ‘turn off’ arbitrary couplings. Then, we analyze the errors of our decoupling method and prove that the errors are ignorable when a sequence of decoupling gates are applied on non-nearest-neighboring qubits. We verify the efficiency of our decoupling method using the numerical simulations, which are well-matched with the theoretical predictions. Using 99.6% fidelity isolated CNOT and 99.89% single-qubit gates, we obtain a fidelity of 97.8% with the CNOT implementation in a five-qubit system over 14.84 ns.